# Reduced-Complexity Artificial Neural Network Equalization for Ultra-High-Spectral-Efficient Optical Fast-OFDM Signals

## Abstract

**:**

## 1. Introduction

## 2. Impact of Directed-Detected Optical Fast-OFDM Signals over AWGN Using Linear Equalization

^{−3}when using 4-ASK is 18.5 dB, 25.5 dB for 8-ASK, and 36 dB for 16-ASK. It should be noted that simulated results agree very well with the analytical results reported in [6], which confirms the validity of the used model.

## 3. ANN and IVSTF Nonlinear Equalizers

## 4. Direct-Detected Optical Fast-OFDM System Model Equipped with NLEs and Performance over SMF

^{®}simulation platform. Similar equalizers have been previously employed in [11,14], which validates the model used in this work. Moreover, the Fast-OFDM system was modulated using 4-, 8- and 16-ASK signal formats at a signal capacity of 9.69, 14.53 and 19.3 Gb/s, respectively, for both equalizers using 64 sub-carriers and 1000 Fast-OFDM symbols. The transmission-reach of the developed system was set at 640 km (8 spans with a fiber-link length of 80 km). The length of CP was set at 25% to ensure effective elimination of inter-symbol interference [28,29]. At the receiver-end of the simulation set-up a single low pass filter (LPF) unit was employed having 3 dB bandwidth of approximately 3 GHz. For optical amplification per span, Erbium-doped fiber amplifiers (EDFAs) were used having a realistic noise figure of 6 dB.

^{2}dispersion slope, 0.11 ps/km 0.5 polarization-mode-dispersion coefficient, 2.69 × 10-20 m

^{2}/W Kerr-induced nonlinearity coefficient, and 80 μm

^{2}effective core area. The key simulation parameters for the developed ANN-based Fast-OFDM transmission model are depicted in Table 1.

^{−3}(the selected forward-error-correction limit at 10

^{−9}) the maximum transmission-reach is at about 380 km, 240 km, and 200 km for 4-, 8- and 16-ASK modulation, respectively. This can be explained by the fact that a higher level of modulation that carry higher data rate increases the SNR on Fast-OFDM sub-carriers, due to the increased amplitude distortions induced by the combined effects of fiber chromatic dispersion and nonlinearity at higher transmission distances.

## 5. ANN vs. IVSTF in Direct-Detected Optical Fast-OFDM

## 6. Computational Complexity Analysis

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Optical signal-to-noise ratio (OSNR) vs. bit-error-rate (BER) performance of optical Fast-orthogonal frequency division multiplexing (Fast-OFDM) over an additive white Gaussian noise (AWGN) channel.

**Figure 2.**(

**a**) Optical Fast-OFDM received diagram showing the equalizer that is based on IVSTF [11]. (

**b**) 16-ASK optical Fast-OFDM received diagram illustrating the ANN sub-neural network equalizer. LPF: low-pass filter; ADC: analogue-to-digital converter; CP: cyclic prefix; DCT: Discrete-Cosine Transform; NLE: nonlinear equalizer; ANN: artificial neural network; n: neuron; MMSE: minimum mean square error; HCD: nonlinear system chromatic dispersion.

**Figure 4.**BER vs. transmission distance for 9.69-Gb/s optical Fast-OFDM at optimum launched optical power of −6 dBm for Volterra-series transfer function (IVSTF)/ANN-NLEs and without (W/O) using NLE.

**Figure 5.**BER vs. optical Fast-OFDM sub-carrier index, with IVSTF-NLE, ANN_NLE and without utilizing ANN at 320 km of fiber transmission.

**Figure 6.**Received optical power vs. transmission distance for 9.69-Gb/s optical Fast-OFDM without (W/O) using NLE.

**Figure 7.**Effect of DAC/ADC components on 4-ASK optical Fast-OFDM transmission performance with the use of IVSTF equalizer, with ANN equalizer and W/O ANN at a signal bit rate of 9.69-Gb/s for a transmitted power of −6 dBm: (

**a**) Quantization bit vs. Distance. (

**b**) Clipping ratio vs. Distance.

**Figure 8.**Computational complexity comparison between ANN-NLE and IVSTF-NLE versus the number of sub carriers, whereas the M-ASK modulation formats (M = 4, 8, and 16) corresponds to the ANN-NLE FLOPS and the 1 span, 10 span and 20 spans corresponds for the IVSTF-NLE FLOPS.

Parameter | Description & Unit |
---|---|

Signal modulation format | 4-, 8-, 16-ASK |

Signal data bit-rate | 9.69, 14.53, 19.37 Gb/s |

Operating wavelength | 1550 nm |

Number of sub-carriers | 64 |

Cyclic prefix (CP) length | 25% |

Forward-error-correction | 7% |

ANN training vector length | 5% |

Photo-detector type | PIN |

PIN sensitivity | −19 dBm |

DAC/ADC sampling rate | 6.25 GS/s |

DAC/ADC quant. bits | 7 |

DAC/ADC clipping ratio | 13 dB |

LPF roll-off function | Bessel-Thomson |

LPF 3 dB bandwidth (order) | 3 GHz (2nd order) |

EDFA gain (noise figure) | 16 dB (6 dB) |

SSMF span (length) | 8 (80 km) |

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**MDPI and ACS Style**

A. Jarajreh, M. Reduced-Complexity Artificial Neural Network Equalization for Ultra-High-Spectral-Efficient Optical Fast-OFDM Signals. *Appl. Sci.* **2019**, *9*, 4038.
https://doi.org/10.3390/app9194038

**AMA Style**

A. Jarajreh M. Reduced-Complexity Artificial Neural Network Equalization for Ultra-High-Spectral-Efficient Optical Fast-OFDM Signals. *Applied Sciences*. 2019; 9(19):4038.
https://doi.org/10.3390/app9194038

**Chicago/Turabian Style**

A. Jarajreh, Mutsam. 2019. "Reduced-Complexity Artificial Neural Network Equalization for Ultra-High-Spectral-Efficient Optical Fast-OFDM Signals" *Applied Sciences* 9, no. 19: 4038.
https://doi.org/10.3390/app9194038